正态逻辑标记自然演绎中的命题量词

Log. J. IGPL Pub Date : 2019-11-25 DOI:10.1093/JIGPAL/JZZ008
Matteo Pascucci
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引用次数: 0

摘要

本文关注的是在Basin, Matthews和Viganò开发的模态逻辑的标记自然演绎框架中对命题量化的处理。我们提供了一个基本演算的详细分析,可用于最小正态多模态系统的证明理论渲染与命题的稳定域上的量化。此外,我们考虑通过关系理论和领域理论获得的基本演算的变化,允许在可能不稳定的命题领域上进行量化。本文的主要结果是不利用反证法的标记演算的片段具有丘奇-罗瑟性质和强归一化性质;将吉拉德的可约候选者方法与λ演算的标记语言相结合,对模态证明的结构进行了编码,得到了这一结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Propositional quantifiers in labelled natural deduction for normal modal logic
This article concerns the treatment of propositional quantification in a framework of labelled natural deduction for modal logic developed by Basin, Matthews and Viganò. We provide a detailed analysis of a basic calculus that can be used for a proof-theoretic rendering of minimal normal multimodal systems with quantification over stable domains of propositions. Furthermore, we consider variations of the basic calculus obtained via relational theories and domain theories allowing for quantification over possibly unstable domains of propositions. The main result of the article is that fragments of the labelled calculi not exploiting reductio ad absurdum enjoy the Church–Rosser property and the strong normalization property; such result is obtained by combining Girard’s method of reducibility candidates and labelled languages of lambda calculus codifying the structure of modal proofs.
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